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GATE 2021 ME (ME1) – Question 20

Metrology and Inspection · Interferometry, form and finish measurement · 1 mark · Multiple choice

Consider the surface roughness profile as shown in the figure. The center line average roughness ($R_a$, in $\mu$m) of the measured length ($L$) is

Surface profile alternating between +1 and −1 micrometre over equal 4-unit intervals. See the attached source image.
  1. 0
  2. 1
  3. 2
  4. 4

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Show answer and explanation

Correct answer: (B) 1

Explanation

Centre-line average roughness averages the absolute height: $R_a=L^{-1}\int_0^L|y|dx$. The absolute height is 1 μm on every segment.

Thus **Rₐ=1 μm (B)**. Signed heights average to zero, but roughness uses absolute deviations.